My Math Forum  

Go Back   My Math Forum > Math Forums > Math Books

Math Books Math Book Forum - Math books, ebooks, references


Reply
 
LinkBack Thread Tools Display Modes
February 8th, 2013, 08:41 PM   #1
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,473
Thanks: 884

Math Focus: Elementary mathematics and beyond
Book on elementary number theory

Any recommendations for a good book on elementary number theory, preferably something that lays a solid foundation for continuing study in the field?
greg1313 is offline  
 
February 8th, 2013, 08:48 PM   #2
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,155
Thanks: 461

Math Focus: Calculus/ODEs
Re: Book on elementary number theory

I have (but have not studied yet...but someday! ) "An Introduction to the Theory of Numbers" by G.H. Hardy and E.M. Wright, Fifth Edition. I have seen it highly recommended by others both for accessibility and coverage.
MarkFL is offline  
February 8th, 2013, 11:15 PM   #3
Math Team
 
mathbalarka's Avatar
 
Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Re: Book on elementary number theory

Quote:
Originally Posted by greg1313
Any recommendations for a good book on elementary number theory, preferably something that lays a solid foundation for continuing study in the field?
MarkFL's suggestion is good if you want to learn NT rigorously.

Try Crandall & Pomerance if you want to get an introduction to computational number theory and some analytical number theory.
mathbalarka is offline  
February 12th, 2013, 07:45 AM   #4
Senior Member
 
Joined: Aug 2010

Posts: 195
Thanks: 5

Re: Book on elementary number theory

Hardy and Wright's book is certainly a quality text, but it memory serves, it lacks exercises and is an older book. If you actually want to learn number theory, you need to do a lot of problems. You might consider Silverman's Friendly Introduction to Number Theory (the third edition is particularly inexpensive now that the fourth is out), it can be a bit fluffy, but it tries to guide readers through figuring things out on their own. It also has a bit more of an algebraic and geometric flavor.

Ultimately, I think it is useful to "graduate" to more advanced books as quickly as possible. Much of the truly excellent exposition on number theory is written at the beginning graduate level. I recommend getting copies of:

Apostol Introduction to Analytic Number Theory
Ireland and Rosen A Classical Introduction to Modern Number Theory

even if only to decorate your shelves for a little while. Apostol's book is actually fairly elementary and only really requires some fairly basic analysis. Ireland and Rosen steadily assume more and more abstract algebra but start out fairly modest (you should know what a principle ideal domain is before starting this book), but is easily my favorite non-expert book on number theory. In the end, you should probably also get a copy of Hardy and Wright's book, as it is an excellent reference, especially when starting out.
Turgul is offline  
February 12th, 2013, 08:31 AM   #5
Math Team
 
mathbalarka's Avatar
 
Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Re: Book on elementary number theory

Quote:
Originally Posted by Turgul
Apostol Introduction to Analytic Number Theory
Ireland and Rosen A Classical Introduction to Modern Number Theory
Yes, I thought about recommending those but that depends if greg1313 want to learn number theory rigorously. I'm reading Ireland & Rosen too so I think it requires a little knowledge on Abstract Algebra. If he wants to learn it, I would suggest Dummit & Foote.

Quote:
Originally Posted by Turgul
Apostol's book is actually fairly elementary and only really requires some fairly basic analysis.
Yes. I am reading Iwaniec & Kowalski and highly recommend for detailed study on ANT. How about the two volume H. Cohen ? I haven't started it yet so I don't know how much appropriate it would be. @Gregory : Do you know modular arithmetic and p-adics?
mathbalarka is offline  
January 18th, 2014, 12:54 AM   #6
Newbie
 
Joined: Oct 2013
From: Bangladesh

Posts: 4
Thanks: 0

Math Focus: Number Theory, Combinatorics
Re: Book on elementary number theory

If you 'really' want to study number theory, you need a theory book and also a book with a lot of challenging problems. Among theory books, I think 'Elementary Number Theory' (fifth edition) by David Burton is the best available online. As a problem book, I would highly recommend both of '104 number theory problems' and 'Number Theory: Structure, examples and problems' by Titu Andresscu These two books are Olympiad oriented and can really give you a greater insight into the beauty of number theory.
mutasimmim is offline  
January 20th, 2014, 07:41 PM   #7
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 932

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Book on elementary number theory

Ireland & Rosen is what I learned number theory from, but I don't recommend it for beginners. It's better for a second course in (algebraic) number theory. Similarly, I find Apostol too advanced. In a pinch you could start with Hardy & Wright but you won't get far if you lack other experience.

The other suggestions are probably more appropriate.
CRGreathouse is offline  
January 21st, 2014, 12:15 AM   #8
Math Team
 
mathbalarka's Avatar
 
Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Re: Book on elementary number theory

I am trying Iwaniec & Kowalski now, do you think it's good for me?
mathbalarka is offline  
January 21st, 2014, 08:46 AM   #9
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 932

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Book on elementary number theory

Quote:
Originally Posted by mathbalarka
I am trying Iwaniec & Kowalski now, do you think it's good for me?
I haven't read it, sorry.
CRGreathouse is offline  
January 21st, 2014, 08:52 AM   #10
Math Team
 
mathbalarka's Avatar
 
Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Re: Book on elementary number theory

I see. What did you use for combinatorial number theory then?
mathbalarka is offline  
Reply

  My Math Forum > Math Forums > Math Books

Tags
book, elementary, number, theory



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
What to include on a first elementary number theory course? matqkks Number Theory 2 June 17th, 2013 10:40 AM
Number theory book zelmac Math Books 4 October 11th, 2012 02:34 AM
2 elementary number theory problems.... earth Number Theory 5 October 9th, 2010 05:54 AM
elementary number theory without zero or negative numbers 2 tinynerdi Number Theory 0 November 29th, 2009 11:01 PM
elementary number theory without zero or negative numbers tinynerdi Number Theory 0 November 29th, 2009 10:25 PM





Copyright © 2017 My Math Forum. All rights reserved.